For a decent make of outdoor socket with RCD protection, you’re looking at around £60, the circuit breaker in the MCB in the consumer unit is another £10, cable, clips, and drilling to the outside to fit, probably a few hours work. I’d say it was probably about the going rate for a qualified spark
Looks like the Hager board has a couple of RCBOs already fitted so would probably make more sense to fit another one for the outside socket instead of an RCD protected socket – overall less expensive and the whole cable run for the “fuse box” is protected as well as whatever is plugged into the outside socket.